Ramond unitarity conjecture for minimal W-algebra highest weight modules

Let $W^k_{\min}(\mathfrak g)$ be the minimal $W$-algebra and let $L^W_R(\nu,\ell)$ denote a Ramond twisted highest weight module. Let $A_R(k,\nu)$ be the Ramond analogue of the conformal-weight bound, and call $\nu$ Ramond extremal when it satisfies the Ramond extremality condition. The already established unitary modules are

$$\left\{L^W_R(\nu,\ell)\mid \nu\text{ is not Ramond extremal},\ \ell\ge A_R(k,\nu)\right\}.$$

Ramond unitarity conjecture. The set of unitary highest weight modules over $W^k_{\min}(\mathfrak g)$ is the union of

$$\left\{L^W_R(\nu,\ell)\mid \nu\text{ is not Ramond extremal},\ \ell\ge A_R(k,\nu)\right\}$$

and

$$\left\{L^W_R(\nu,A(k,\nu))\mid \nu\text{ is Ramond extremal}\right\}.$$

The non-Ramond-extremal case is stated as a theorem, whereas the source explicitly says that unitarity in the Ramond-extremal case is not known.